FORT WORTH — Since its opening here in 1972, the Kimbell Art Museum has been envied the world over not only for having one of the world’s choicest collections of art, but for having one of its finest museum buildings.

The collection is certainly special. Despite boasting not only a scintillating group of European Old Masters and early Moderns but strong holdings in Asian, African, Ancient, and pre-Columbian art, it has only around 350 works. (To compare, Boston’s Museum of Fine Arts has 450,000.)

In other words, the Kimbell buys only the best, and it has an unrestricted endowment of $400 million to help it do so. Recent jaw-dropping additions include Poussin’s “Sacrament of Ordination” — one of the most important Old Master paintings to come on the market in several decades — and the first extant painting by Michelangelo. Better yet, it keeps the vast majority of what it owns on display.

But as I said, the Kimbell’s other big draw is its building. Designed by Louis Kahn, it was completed two years before his death in 1974. (Kahn’s best museum building in New England, and the last of his career, the Yale Center for British Art in New Haven, was finished after his death.)

Justly famous for its ingeniously simple harnessing of natural light, Kahn’s Kimbell building is essentially a succession of six long cycloid vaults, each divided into three equal lengths, framed in concrete, clad in travertine, and judiciously interrupted to create courtyards and open entrances.

Unfortunately, like so many other museum buildings in this era of accessibility, outreach, and endless institutional expansion, it quickly came to feel too small. Every time the Kimbell hosted a temporary exhibition, large parts of the permanent collection (which was all the while quietly expanding) had to be taken down.

The space constraints were already apparent back in the mid-1980s. But a controversial plan then simply to extend Kahn’s modular vaults was rejected: Don’t meddle, was the message, with perfection.

‘The museum has as many moods as there are moments in time, and never . . . will there be a single day like any other.’

Two decades on, the Kimbell has at last acquired the new space it needs. Its new building, situated 300 feet away across a grassy lawn, opened late last year. It was designed by Renzo Piano, an Italian architect who once worked for Kahn and is particularly well known in Boston for taking on sensitive museum commissions: Last year the Isabella Stewart Gardner Museum opened a new building designed by Piano; and later this year, the Harvard Art Museums will open its own Piano-designed renovation and expansion on Quincy Street in Cambridge.

Piano is well-paid, to be sure, but you have to admire his willingness to wade into no-win situations. The Gardner commission involved meddling with an all-but sacred institution — one that whispered “noli me tangere” (“touch me not”) to anyone who approached.

The Harvard project, too, involves taking on not only an admired Georgian-revival building (the old Fogg Art Museum, designed by the venerable firm of Shepley Bulfinch Richardson & Abbott), but the museum’s next-door neighbor, which just happens to be the only building in America built by the great modernist pioneer Le Corbusier.

Piano gets these commissions because of his sensitivity, his attention to detail, and his willingness to go through the motions of humbling himself before the hallowed past. But you have to think there is a high dose of competitiveness in him, too.

Now, in Fort Worth, he not only goes mano-a-mano with the almost universally admired Louis Kahn, but with the acclaimed architects of two adjacent museums: the Amon Carter Museum of American Art, designed in 1961 by Philip Johnson, champion of the International Style, and the Modern Art Museum of Fort Worth, designed in 2002 by Japan’s Tadao Ando. (Ando is another familiar and closely watched name in New England: His ambitious expansion to the Sterling and Francine Clark Art Institute will open later this year, the second phase in a project that has already seen the construction of his Stone Hill Center, a short walk up the hill from the Clark’s main buildings.)

The three Fort Worth museums together form one of America’s most potent and rewarding museum precincts. But of the three, each remarkable in its own way, there’s no question that the Kimbell is the jewel, and thus the one that demands the most delicate handling. So how does the Piano building measure up to the original Louis Kahn?

Extremely well. Piano’s pavilion is — deliberately, you feel — unprepossessing from the outside. It has a recessed glass entrance flanked on either side by a long, low, white concrete façade that faces the Kahn building across the lawn. It has a flat, overhanging glass roof elaborately (if invisibly) bedecked with aluminum louvers, glass, solar cells, and stretched fabric scrims. And at either end, it has rows of columns, supporting heavy roof beams made of gray laminated Douglas fir.

The squared-off concrete columns, just 10 feet apart, cast diagonally striped shadows, in the manner of Greek temples — although the comparison is somewhat invidious: Their spacing and the heaviness of the roof beams create a top-heaviness that runs counter to the balanced proportions of the Greeks.

But this pavilion, which holds a large, transparent lobby and galleries bathed in filtered natural light on either side, is just one part of the new building. The other part, connected by two glass walkways (shades of Piano’s glass “umbilical cord” connecting his addition to the Gardner Museum), is behind the first, and partially built into an artificial hill. It holds a beautiful 298-seat auditorium, education facilities, a library, and darker galleries for light-sensitive works, mostly from Asia.

There are many deliberate and respectful rhymes with the Kahn building. The symmetrical stairwells leading down to the auditorium, for instance, echo a similar device at the back entrance to the original building. The concrete walls of the façade, made white by a 2 percent addition of titanium and smooth by unprecedentedly minimal seams, are especially sensuous.

BUT OF COURSE, it is hard to get too excited about concrete when you are only a few feet from so many artistic treasures. The Kimbell’s Old Master and Asian collections have been displayed for now in the new Piano Pavilion, where they look good, while the Kahn building has the more modern works from the collection, as well as a temporary exhibition of modern art from the Art Institute of Chicago.

The show’s title is “The Age of Picasso and Matisse.” And although it is in fact a compelling overview of the main movements of early Modernism, it delivers handsomely on the promise of its title. Matisse’s masterpiece “Bathers by a River” hangs at one end of Kahn’s long vaults and has probably never looked better. Also on view are one of his loveliest late works, “Daisies,” and several important paintings from his early years in Nice.

Matisse’s younger Spanish rival is represented by major pieces from various stages of his career, ranging from his 1906 breakthrough summer in Gosol (the Kimbell, wouldn’t you know it, has its own Picasso from the same year) to the various phases of Cubism, neo-classicism, biomorphic surrealism, and beyond.

Beautifully installed by the Kimbell’s senior deputy director George Shackelford, who went to Forth Worth in early 2012 after leaving his post as chair of the art of Europe at Boston’s MFA, “The Age of Picasso and Matisse” is unusually fine for a show selected from one museum’s permanent collection. (Ironically, these works were made available only because the Art Institute of Chicago has had to close its Modern Wing for unplanned repairs. That building was designed by none other than Renzo Piano.)

But no matter what the show of the moment, the Kimbell’s permanent collection will always be the main draw for out-of-state visitors. It’s hard to know where to begin with so fine a collection. But aside from the aforementioned Poussin and Michelangelo, don’t overlook George de la Tour’s “The Cheat With the Ace of Clubs,” the Frenchman’s take on Caravaggio’s early masterpiece, “The Cardsharps” — which is also in the collection — and Duccio’s “The Raising of Lazarus,” an astonishing thing.

APAVILION IS, ALMOST BY DEFINITION, a pleasant place to be. The Kimbell’s Piano Pavilion, which cost $135 million, is actually the latest in a series of similar museum buildings that Piano has been perfecting over many years, most notably at the Menil Collection in Houston, the Beyeler Foundation in Basel, Switzerland, and the Nasher Sculpture Center up the road in Dallas.

All of them are low-slung and rectilinear, and at once rational (you can see how they were made) and poetic (they harvest natural light, connecting visitors to the many moods of the outside world, even as they soften and shape those moods).

If Piano’s Kimbell addition has attracted criticism, or praise that is only lukewarm, it may be partly because of its enforced subservient role (in situations like this, Piano must always approach on bended knee). But it’s also, I think, because of a prevailing nostalgia for classical modernism that can overpower clear thinking.

Kahn, who said his building was inspired by “Roman greatness,” was one of the greatest exponents of this kind of classical modernism. From the outside, the internal form of his physical design is clearly deducible. This kind of conceptual transparency, beloved by die-hard modernists, is linked to the modernist dictum of form following function.

But it’s worth noting that, unlike Piano’s best buildings, Kahn’s building is not literally transparent at all. From without, it is mostly opaque — all concrete and travertine. There are hardly any externally obvious windows, and the building is not, in the final analysis, especially attractive: You see it from the street and wonder if it might exist to provide off-site storage, or hold classified government files.

It’s only from within that Kahn works his enchantment. And he does it all, amazingly, with light.

At the top of Kahn’s vaults, where their arches would meet, he left a long, continuous slit that lets in natural light from directly overhead. Just below this slit, he installed pierced, curving metal reflectors that spread that light down the insides of the vault.

Thus, the problem of letting in direct and damaging light was avoided, even as the lovelier qualities of natural light were retained and enhanced.

To achieve such lucidity in a building so devoid of exterior windows was, you feel, a kind of miracle. Kahn knew it, and delighted in what he had achieved: “The museum,” he chirped, “has as many moods as there are moments in time, and never as long as the museum remains as a building will there be a single day like any other.”

Sunlight, which is poetic, can also be a disinfectant. But there is a difference between the poetry of light, so deftly evoked by Kahn, and the ideal of transparency that, in architecture as in government, has always had a political dimension.

Transparency is essential to a style of architecture that was devoted to banishing fear, and with it, mystery. It is predicated on no secrets, no dungeons, no barbaric bureaucracies, on everything being lucid, predictable, and accessible. As an ideal, it is cherished by modernists as an antidote to the (quintessentially modern) predicament of Kafka’s protagonist in his parable, “Before the Law,” who is told, after years of thwarted striving: “This door was intended only for you. I am now going to shut it.”

In late-20th-century architecture, perhaps the most famous manifestation of the “transparency doctrine” (as distinct from the literal transparency of glass houses by Mies van der Rohe and Philip Johnson) is Paris’s Centre Georges Pompidou, the museum designed by Renzo Piano, Richard Rogers, and Gianfranco Franchini.

The Pompidou was completed just five years after the Kimbell. Its architects were less concerned with actual light than with advertising an ideal of transparency. Performing the architectural equivalent of airing dirty laundry, they put most of the building’s mechanical guts — color-coded pipes and ducts for plumbing, climate control, and electrical wiring — on the outside, for all to see.

They turned the lucid poetry of Kahn and his fellow proponents of classical modernism into what was effectively a rousing political slogan.

The Pompidou, according to the jury of the Pritzker prize for architecture (which was awarded to Piano in 1998 and Rogers in 2007), “revolutionized museums, transforming what had once been elite monuments into popular places of social and cultural exchange.”

People may still feel ambivalent about the Pompidou as a working museum. But its impact as a manifestation of the new way to think about museums — as “popular places of social and cultural exchange” — cannot be overstated.

If Piano is partly responsible for this shift, he is certainly reaping the benefits, as measured in museum commissions. But he has also moderated and refined his aesthetic in ways it is hard not to admire. He has brought it closer to Kahn’s, so that today his buildings seem as sensitive and responsive to the so-called “elitism” (some would say the “poetry”) of earlier museums as to the politically charged populism of the new.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.

Thanks & Welcome to Globe.com

You now have unlimited access for the next two weeks.

BostonGlobe.com complimentary digital access has been provided to you, without a subscription, for free starting today and ending in 14 days. After the free trial period, your free BostonGlobe.com digital access will stop immediately unless you sign up for BostonGlobe.com digital subscription. Current print and digital subscribers are not eligible for the free trial.